1. Field of the Invention
The subject invention relates to strain gages, to transducers, and to methods of making strain gages and tranducers, including strain gages and transducers of semiconductor material.
2. Information Disclosure Statement
The following disclosure statement is made pursuant to the duty of disclosure imposed by law and formulated in 37 CFR 1.56(a). No representation is hereby made that information thus disclosed in fact constitutes prior art, inasmuch as 37 CFR 1.56(a) relies on a materiality concept which depends on uncertain and inevitably subjective elements of substantial likelihood and reasonableness and inasmuch as a growing attitude appears to require citation of material which might lead to a discovery of pertinent material though not necessarily being of itself pertinent. Also, the following comments contain conclusions and observations which have only been drawn or become apparent after conception of the subject invention or which contrast the subject invention or its merits against the background of developments which may be subsequent in time or priority.
The change of resistance of diffused silicon resistors with strain is a phenomenon well known and utilized for semiconductor strain gages. The magnitude of resistance change depends on the strain level, on the doping concentration and type and on the crystallographic orientation of the gages. For a given doping level the resistance change is given by the following equation: ##EQU1## Where .DELTA.R=resistance change
R.sub.o =gage resistance PA1 .sigma.=stress PA1 .pi..sub.L =longitudinal piezoresistive coefficient PA1 .pi..sub.T =transverse piezoresistive coefficient
For P-type gages (with hole conductivity) tension will cause a positive resistance change, compression a negative change.
For N-type gages (with electron conductivity) tension will cause a negative resistance change. Compression will cause a positive change.
The highest longitudinal piezoresistive coefficient is obtained if the gages are oriented in the &lt;1-1-1&gt; crystallographic direction. This is the reason why many of the diffused silicon devices or also bulk silicon bar gages are using (1-1-0) silicon wafers with gages oriented in the &lt;1-1-1&gt; direction. A pressure sensing device utilizing similar strain gages is arranged in the form of a diaphragm or a beam which deform by application of pressure in such a way that two gages are in tension and two gages in compression, all connected in Wheatstone bridge configuration. The changes in resistance are causing a change in zero of the bridge proportional to the pressure. A half bridge with one gage in tension and one in compression is also possible. The value of the piezoresistive coefficients in the &lt;1-1-1&gt; orientation is: ##EQU2##
The value of .pi..sub.11 and .pi..sub.12 is very small compared to .pi..sub.44. Therefore, we can approximate the piezoresistive coefficients as: ##EQU3##
We can see that the value of the transverse piezoresistive coefficient is only 50% of the longitudinal one.
For many pressure sensor applications it is desirable to use (1-0-0) silicon because of its crystallographic symmetry permitting to etch symmetrical shapes. The &lt;1-1-0&gt; direction gives the highest piezoresistive coefficient in the (1-0-0) plane. The values of the piezoresistive coefficients are: ##EQU4## and when neglecting .pi..sub.11 and .pi..sub.12 as very small compared to .pi..sub.44 : ##EQU5##
The values .pi..sub.L and .pi..sub.T are the same only with opposite signs and with absolute value 25% lower than for the &lt;1-1-1&gt; direction.
The fact that the values of .pi..sub.L and .pi..sub.T are identical with opposite signs can be used with advantage for sensor configurations where one or two gages are in longitudinal tension (compression) and one or two gages in transverse tension (compression) again connected in a Wheatstone bridge configuration which changes zero with pressure.
The above applies both for diffused gages and for so-called bar gages etched out of bulk silicon wafers and epoxy or glass bonded to the surface of a metal diaphragm or beam. Whatever the configuration, we try to place the gages always in an area with a predominantly uniaxial stress, with one or two gages of the bridge in tension and one or two gages of the bridge in compression.
Because of the symmetry of the cubic cell it is understood that plane (1-0-0) can mean any of the base planes of unit cell (010,001, 100 , 010 , 001) and direction &lt;1-0-0&gt; can mean any direction perpendicular to above base planes. The same applies for planes and directions (1-1-0) and &lt;1-1-1&gt;.
For a calculation of values of piezoresistive coefficients, reference may be had to Integrated Silicon Device Technology, Vol. V, by Research Triangle Institute, Publication #AD605558 (July 1964).
An article by W. G. Pfann, R. N. Thurston, entitled Semiconductor Stress Transducers Utilizing Shear Piezoresistance Effects, Journal of Applied Physics, Vo. 32, No. 10 (Oct. 1961), pp. 2008-2019, also provides calculations of piezoresistive coefficients. The 110/100 orientation of gages is mentioned as "insensitive to transverse stresses" and a bridge for a load cell is proposed which would be sensitive only to stresses parallel to one arm of the bridge. All configurations are explored only for load cell applications and torsion load cells.
An article by A. C. M. Gieles, G. H. J. Somers, entitled Miniature Pressure Transducers With A Silicon Diaphragm, Philips Tech. Review, 33, No. 1 (1973), pp. 14-20, deals with a (110/001) configuration of gages for a diffused and back-etched diaphragm configuration (silicon diaphragm). The purpose was to enable bringing all four gages as close together as possible and thus minimizing the effect of temperature changes on bridge balance. The idea has been apparently rejected for two reasons: Strong direction dependent mechanical stress in the (110) plane affecting the very thin diaphragm and the stability of the gage and because of variable contact resistance ("junction resistance") of the pads in the highly strained part of the diaphragm. This led to the use of diaphragms parallel to the (111) plane and gages in &lt;110&gt; direction (tension and compression).